- Subsequence
In
mathematics , a subsequence of somesequence is a new sequence which is formed from the original sequence by deleting some of the elements without disturbing the relative positions of the remaining elements.Formally, suppose that "X" is a set and that ("a""k")"k" ∈ "K" is a sequence in "X", where "K" = {1,2,3,...,"n"} if ("a""k") is a finite sequence and "K" = N if ("a""k") is an infinite sequence. Then, a subsequence of ("ak") is a sequence of the form where ("nr") is a strictly increasing sequence in the index set "K".
Example
As an example,:is a subsequence of:,with corresponding index sequence <3,7,9,11>.
Given two sequences "X" and "Y", a sequence "G" is said to be a "common subsequence" of "X" and "Y", if "G" is a subsequence of both "X" and "Y". For example, if: and:then common subsequence of "X" and "Y" could be:
This would "not" be the "longest common subsequence", since "G" only has length 3, and the common subsequence < B,E,E,B > has length 4. The longest common subsequence of "X" and "Y" is < B,E,G,C,E,B >.
Applications
Subsequences have applications to
computer science , especially in the discipline ofBioinformatics , where computers are used to compare, analyze, and storeDNA strands.Take two strands of DNA, say :
ORG1 = ACGGTGTCGTGCTATGCTGATGCTGACTTATATGCTA
ORG2 = CGTTCGGCTATCGTACGTTCTATTCTATGATTTCTAASubsequences are used to determine how similar the two strands of DNA are, using the DNA bases:
adenine ,guanine ,cytosine andthymine .ubstring vs. subsequence
In computer science, "string" is often used as a synonym for "sequence", but it is important to note that "
substring " and "subsequence" are not synonyms. Substrings are consecutive parts of a string, while subsequences need not be. This means that a substring of a string is always a subsequence of the string, but the subsequence of a string is not always a substring of the string. [cite book | last = Gusfield | first = Dan | origyear = 1997 | year = 1999 | title = Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology | publisher = Cambridge University Press | location = USA | id = ISBN 0-521-58519-8 | pages = 4]ee also
*
subsequential limit
*limit superior and limit inferior
*longest common subsequence problem
*longest increasing subsequence problem
*Erdős–Szekeres theorem References
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